You'll need to try to find the pattern that applies here. Find the 1st, 2nd, 3rd, 4th and 5th derivatives. Is a pattern evident?
n=1: first derivative of (sin x)^3 is 3(sin x)^2*cos x (which is a product)
n=2: second deriv. of (sin x)^3 is 3(sin x)^2*(-sin x) + (cos x)*(6sin x cos x)
Please find the 3rd, 4th and 5th derivatives. Then try to recognize a pattern in the derivatives governed by the counter "n".